[Discussion] Patch Notes - Page 117

- RF's AP coefficient has been decreased from 0.3 to 0.2;
- Kayle's passive no longer gives her bonus AD (in fact, it sucks now);
- Divine Blessing's AP coefficient has been decreased from 0.5 to 0.35;
- Reckoning's AP coefficient has been increased from 0.8 to 1.0.

Old Kayle got the following for every 100 AP:
- 45 bonus damage for her autoattack (30 from RF, 15 from her passive);
- 80 damage for her nuke;
- 50 health for her heal.

New Kayle gets the following for every 100 AP:
- 20 bonus damage for her autoattack (20 from RF);
- 100 damage for her nuke;
- 35 health for her heal.

Considering that most of Kayle's damage is autoattack damage, AP isn't even half as good now as it used to be. If you look at damage output numbers, hybrid items like Gunblade are no longer good on her (I'll prove it with math in section 3).

Let's assume you agree with me and build Zerk Greaves and Nashor's Tooth on Kayle. Total cost is 3,805 gold, which I'll assume you get by level 8. What do you buy after that, an Infinity Edge (3,830 g), a Wit's End + Malady combo (3,975 g), or a Gunblade (3,625 g)?

First, let's see what your damage output looks like (assuming 100% uptime for Righteous Fury) for when you start buying each item. If IE, you want a Pickaxe. If Wit's End + Malady, you want a Recurve Bow. If Gunblade, you want a Pickaxe too.
Base autoattack damage: 74
Righteous Fury damage: 50 (+55 AP * 0.2) = 61
Attack speed: 1.381 (6.905 attacks per 5 seconds)
Critical chance: 0% (0 crits per 5 seconds)

DPS (against a 0 Armor, 0 MRes target): (74 + 61)*6.905 / 5 = 186.435

With Recurve Bow: Attack speed increases to 1.637 (8.185 attacks per 5 seconds). DPS increases to 220.995
With Pickaxe: Autoattack damage increases by 25. DPS increases to 220.96.

That means, after you have your Nashor's Tooth and Zerk Greaves, you have enough Attack Speed that the Pickaxe and the Recurve Bow are almost equivalent.

Now, let's look at the final picture: you need close to 4,000 g to complete these, so we'll assume you only get that by level 15. By level 15, Kayle will have:
Base autoattack damage: 91 (+80 if IE, + 60 if Gunblade)
Magic damage per hit: (62 if WE&M)
Righteous Fury Damage: 60 (+11 if IE, +16 if WE&M, +26 if Gunblade)
Attack speed: (1.484 if IE or Gunblade, 2.058 if WE&M)
Attacks per 5 secs: (7.42 if IE or Gunblade, 10.29 if WE&M)
Critical chance: (25% if IE, or 1.855 crits per 5 secs)

DPS is calculated as:
(Base autoattack damage + bonus AD + magic damage + Righteous Fury + AP coefficient of RF) * Attacks per 5 seconds / 5 + (Crits per 5 secs)*(Base autoattack damage + bonus AD)*(250% - 100%) / 5

IE DPS: [ (91+80+60+11) * 7.42 / 5] + [1.855 * (91+80) * 1.5 / 5 ] = 454.2895
WE&M DPS: [ (91+62+60+16) * 10.29 / 5] = 471.282
Gunblade DPS: [ (91+60+60+26) * 7.42 / 5] = 351.708

That is to say, DPS of Infinity Edge is almost on par with WE&M, while Gunblade is far (far) behind. Each of these items has a different set of advantages:
- Infinity Edge has the best end-game scaling (add Last Whisper, Phantom Dancer, whatever);
- WE&M provides MRes and suffers less from Thornmail;
- Gunblade adds more to your heal and your nuke, provides a redundant nuke with a slow, and adds lifesteal. I think it isn't close to measuring up.
- Bloodrazor deals % health damage, which is nice against high-HP teams. I didn't do the math for it here because its performance depends so much on who you're fighting.

Pick whichever you need!